Stationary correlations for a far-from-equilibrium spin chain

Abstract

A kinetic one-dimensional Ising model on a ring evolves according to a generalization of Glauber rates, such that spins at even (odd) lattice sites experience a temperature $T_e$ ($T_o$). Detailed balance is violated so that the spin chain settles into a non-equilibrium stationary state, characterized by multiple interactions of increasing range and spin order. We derive the equations of motion for arbitrary correlation functions and solve them to obtain an exact representation of the steady state. Two nontrivial amplitudes reflect the sublattice symmetries; otherwise, correlations decay exponentially, modulo the periodicity of the ring. In the long chain limit, they factorize into products of two-point functions, in precise analogy to the equilibrium Ising chain. The exact solution confirms the expectation, based on simulations and renormalization group arguments, that the long-time, long-distance behavior of this two-temperature model is Ising-like, in spite of the apparent complexity of the stationary distribution.

9 pages

References in corpus (5)

• Free Energy Functional for Nonequilibrium Systems: An Exactly Solvable Case
• Exact Free Energy Functional for a Driven Diffusive Open Stationary Nonequilibrium System
• The effects of violating detailed balance on critical dynamics
• Contrasts between Equilibrium and Non-equilibrium Steady States: Computer Aided Discoveries in Simple Lattice Gases
• Non-equilibrium stationary state of a two-temperature spin chain

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• Nonuniform autonomous one-dimensional exclusion nearest-neighbor reaction-diffusion models
• Nonuniform autonomous one-dimensional exclusion nearest neighbor reaction diffusion models, II